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1)

(a) According to Rebbi Yossi, on Sunday, Rosh Chodesh Sivan, the day they arrived at Har Sinai and on Monday the second, they rested from the journey. On Tuesday, the third, Moshe ascended for the first time and Hashem said "Atem Re'isem ... ve'Ata Im Shamo'a Tishma ... vi'Heyisem Li Segulah ... ve'Atem Tihyu Li Mamleches Kohanim" ... (Sh'mos 19:4-6). In the evening, he returned to tell Yisrael, who replied "Kol Asher Diber Hashem" ... (Pasuk 5).
On Tuesday, the third of Sivan, Moshe reported to Hashem Yisrael's reply, and Hashem responded with "Hinei Anochi Ba Eleicha" ... (Pasuk 9), and ve'Higbalta es ha'Am (the Mitzvah of Hagbalah) ... Lo Siga Bo Yad" ... (Pasuk 12&13).
On Wednesday, the fourth, Hashem said "Lech el ha'Am ve'Kidashtem" (the Mitzvah of Hafrashah) ... "Vayered Moshe min ha'Har (and, on the same morning) ... Vayomer el ha'Am Heyu Nechonim li'Sheloshes Yamim" ... (the Mitzvah of Hafrashah).

(b) "ve'Kidashtem ha'Yom u'Machar" clearly implies that there were only two days Hafrashah, in which case, the Torah would have been given on Friday, and not on Shabbos.

(c) Rebbi Yossi maintains that, in fact, Moshe added one day of Hafrashah.

(d) We know that Hashem agreed with that decision, because the Shechinah did not descend onto Har Sinai until Shabbos, the day Moshe had ordained.

(a) Moshe also separated permanently from his wife and smashed the Luchos - of his own accord.

(b) We know that Hashem agreed with those decisions too, because after telling Moshe (after Matan-Torah) that Yisrael were permitted to return to their wives, He said to him "ve'Ata Poh Amod Imadi".
And with regard to the smashing of the Luchos, He said later (in Ki Sisa) "Asher Shibarta" ... which Chazal explain to imply 'Yeyasher she'Shibarta' - 'Thank you for breaking them!'

(c) Moshe added one day to the original two of Hafrashah, because he Darshened "ha'Yom u'Machar" to imply today like tomorrow. Just like tomorrow is a full twenty-four hour day, so too, today (though this is not a real Derashah - See Tosfos DH 'ha'Yom'). Consequently, he decided to discount today, and to keep two full days, without today - i.e. tomorrow and the day after (Thursday and Friday).
He separated from his wife on the basis of a Kal va'Chomer: if Yisrael, who were only receiving the Shechinah on this one occasion, were told to separate from their wives, then *he*, who would receive the Shechinah on numerous occasions, must certainly be ready for that, whenever he would be called.
Alternatively, because Hashem always spoke with him 'Peh el Peh'. And he smashed the Luchos too, on the basis of a Kal va'Chomer: if already the Korban Pesach, which is just one of the Taryag Mitzvos, is forbidden to a 'Ben-Nechar' (a Jew who has served idols), then how on earth could he give the entire Torah (which was contained on the Luchos) to Yisrael, who were dancing round the Golden Calf? (See Tosfos DH 'u'Mah').

(a) "va'Yaged Moshe es Divrei ha'Am el Hashem" refers, according to Rebbi Yossi b'Rebbi Yehudah, to the Mitzvah of Hagbalah, which Yisrael had accepted on themselves (even though it is only written three Pesukim later - see also Rashi in Chumash, who gives a different interpretation).

(b) "va'Yashev Moshe" ... means that he first told them things that would normally cause one to rebel (Shovav) - i.e. the punishments, and then "va'Yaged Moshe" - he told them the things that attract like Agadah (the rewards due to those who keep the Torah).
Alternatively, "va'Yashev Moshe" means that he first told them the reward (things that make the heart feel settled ('she'Mashivin' ... ), and then "va'Yaged Moshe" - the things that are hard like a bitter herb called 'Gidin' (the punishment).

(a) The author of the Beraisa which says 'Shelishi, Shelishi ba'Chodesh, Shelishi be'Shabbos' - which specifically equates Tuesday with the *third* of the month, clearly holds that Rosh Chodesh fell on *Sunday*, and not on Monday. Consequently, the author must be Rebbi Yossi.

(b) The first Shelishi in the Beraisa refers either to the Mitzvah of Hagbalah, which was commanded on that day, or to the words of Moshe referred to in the previous question.

(a) The author of this Beraisa ('Shishi, Shishi ba'Chodesh' ... ) too, which equates Friday with the *sixth* of the month, must be Rebbi Yossi, because according to the Rabbanan, Friday was the *fifth* of Sivan, and not the sixth.

(b) According to others, 'Shishi' also refers to the day that they left Refidim.

(c) Some say that the Mitzvah of Shabbos, which they were given at Marah (as we know from "Ka'asher Tzivcha Hashem Elokecha" - which was written on the second Luchos), incorporated 'Techumin'; so they could not have traveled on Shabbos.
Consequently, they must have left Refidim on Sunday, the same day that they arrived at Har Sinai.
Whereas according to others, the Shabbos of Marah did not include the Mitzvah of Techumin. Consequently, they were able to travel on Shabbos, in which case, they could have left Refidim on Shabbos, to arrive at Har Sinai on Sunday.

6)

(a) Yisrael left Egypt on a Thursday.

(b) If the fifteenth of Nisan fell on Thursday, that means that Rosh Chodesh Nisan too, fell on Thursday. Consequently (since Nisan is generally a full month), Rosh Chodesh Iyar must have fallen on Shabbos, and (since Iyar is generally a short month) Rosh Chodesh Sivan, on Sunday.

(c) The Rabbanan will say that, even if they did leave Egypt on Thursday, Rosh Chodesh Sivan could still have fallen on Monday - because they made Iyar of that year a full month.

(a) Yisrael arrived at Midbar Sin on Shabbos, and began to grumble about the lack of food (because the remains of the Matzos which they took with them out of Egypt, ran out). We know this from various Pesukim, which inform us that the Man began to fall on the following day, and that the first fall of Man took place on a Sunday.

(b) 'Rishon ...

1. ... le'Ma'aseh Bereishis' - means that the first of Nisan of that year fell on Sunday (the first day of the creation).
2. ... li'Nesi'im' - the day that Nachshon ben Aminadav, the first of the Princes, brought his inaugural offerings for the dedication of the Mizbei'ach.
3. ... li'Kehunah' - means that *that* day - the eighth day of the Milu'im - was the very first time that the Avodah was performed by Aharon and his sons. Until then, it had been performed by the first-born.
4. ... la'Avodah' - means that this was the commencement of the regular Avodas Tzibur - i.e. the twice daily Korban Tamid and the Korban Musaf of Rosh Chodesh - bought with the money of the Terumas ha'Lishkah.
5. ... la'Achilas Kodshim' - means that this was the first time that Kodshim had to be eaten within a Mechitzah; until now, they could be eaten anywhere.

(c) That day was also the first time that the fire came down from Heaven to consume the Korban Tzibur; ... that the Shechinah dwelt in the midst of Klal Yisrael; ... the Kohanim blessed Yisrael; ... that Bamos became forbidden and the first of the months (a distinction which, until now, had been reserved for Tishri).

(d) The Beraisa is speaking about the year after they left Egypt.

(a) Acherim (Rebbi Meir) says in a Beraisa that there are always four days difference between Shevu'os of one year and that of the following year. What he means to say is that if any Rosh Chodesh falls - for example - on Sunday one year, it will fall on Thursday (four days later) the following year (and if it is a leap-year, on Friday, ). This is because the months are bound to follow the same pattern: Nisan full, Iyar short. Sivan full, Tamuz short etc. Consequently, after counting 350 days (which can be divided into full weeks), one is left with four days.
That being the case, if, as the Beraisa declares, Rosh Chodesh Nisan of the second year, fell on Sunday, then Rosh Chodesh Nisan of the previous year - the year they left Egypt - must have fallen on Wednesday.

(b) And if Rosh Chodesh Nisan fell on Wednesday, then Iyar will have fallen on Friday, and Sivan on Shabbos - neither on Sunday, like Rebbi Yossi, nor on Monday, like the Rabbanan?

(c) The Gemara answers that, according to Rebbi Yossi, they arranged one extra full month, so that Rosh Chodesh Nisan of the previous year fell on Thursday (despite the fact that there will only have been three days between the two Nisans - and not four, like Acherim).
And according to the Rabbanan, we will have to say that they even arranged for *two* extra short months, so that Rosh Chodesh will have fallen not on Thursday, but on Friday (so that there were only *two* days between the two Nisans).

(a) If Rosh Chodesh Nisan of the year of the Exodus took place on Friday, then Rosh Chodesh Iyar must have taken place on Sunday, and Rosh Chodesh Sivan, on Monday - like the Rabbanan.

(b) Rebbi Yossi maintains that on Thursday, the fifth Sivan, Moshe built a Mizbei'ach and brought on a sacrifice.

(c) When Rebbi Yossi wrote that Moshe had no time on Erev Shabbos, he meant, not because he was busy with Matan Torah, but because he was busy with the preparations for Shabbos.